T Nation



The physics kind, not a job, mind you.

Here's my question. We've all heard that the energy requirements for running a mile versus walking it are the same. Same amount of distance moved, same amount of energy required. For example, if it takes you 10 minutes to walk the distance at 10kCal/min, then it takes 100kCal to move that distance. If you run it in 5 minutes, supposedly it takes 20kCal/min, so the math works out.

My question is: Isn't this an over-simplification? This assumes that the body is equally efficient at, for example, running twice as fast as one walks. Somehow, this doesn't sit well with me. Thoughts, anyone?

Oh, I just want to make clear I'm not talking about the post-exercise caloric debt, here. Just the actual energy involved. Obviously there would be a much bigger debt running a mile's worth of sprints versus walking a mile.


I agree, it doesnt take into account increase thermal demands, increased vertical displacement etc in gait and THEN there is the increase in Post Exercise Oxygen Consumption. Any other comment or aspect this doesn't ake into account?


It's like comparing apples and oranges. Physics work isn't really related to the modern day use of the word work. Physics work is Force times distance (W=Fd) and force is mass times acceleration, as soon as you stop accelerating, you're doing no work. That means that when you're lifting, you're doing no actual work, cause in most of the big money movements, the bar goes back to where you start from. But if you look at power (work times velocity if I remember right) that's where you get the more general idea of work that people think of when they say they're doing work.


Ikester: Interesting question, bruh. Actually, I hate to be a prick, but actually no Work is done when walking or running (on a flat surface). The vertical distance moved is negligible. Sorry to get so technical, but let's get on with the show.

You're right, though. As far as energy requirements for the activity--whether walking or running--in theory, they are the same. However, it is efficiency of movement that really dictates the discrepancy in energy needs.

Nope, it doesn't sit well with me either, but it's the truth. I don't really know what else to say, Ikester, except that it's true. The difference would be that you could expend more energy in a given time frame exercising at a higher intensity (i.e. running vs. walking).


You're right .. that's a gross simplification.

Look at how we move our body from A to B - perhaps if we slid along as though on wheels we'd do the same amount of work regardless of speed.

But we don't have wheels for feet (at least I don't anyway)

Look at the distance your limbs move in a walking gait vs a running gait.

I'm no expert on the biomechanics of gait by any means, but as I understand it, a particular gait gets less and less efficient as you increase speed, which is why we shift to a different gait (walk to jog, jog to run etc) This means that a comfortable jog is more efficient than an unnaturally rapid walk for example.

Easy way to test this is to walk a certain distance then by way of comparison take the same time to cover the same distance but "run" it, driving your knees up to waist height with each step. You'll clearly do a lot more work with the latter.


Okay, so I wiffed it on the physics terminology. Seems I really did blow the last of my analytical circuits on that physics final all-nighter two years back. Explains why I'm a liberal arts major now, 'eh? :slight_smile:

Anyway, it still sounds suspect to me that the body as efficient at a velocity of, say, '2x', as it is simply at 'x'. If it requires twice as much energy to go twice as fast, doesn't that imply that -all- of the energy is getting converted to movement? That's real suspect, to me. Sounds too much like one of those 'perfect machine' scenaries. What about thermal energy radiation, friction, etc?


I know what you're saying about thermal energy loss and friction. The further up into physics you get, the more you take into account all of these losses in energy due to factors other than the motion measured. Although the effect is less than you'd think, because while thermic energy release gets higher the faster you'd run, frictional effects get lower, because your feet are in contact with the ground for less time, and over longer distances (assuming that your running form gives you long stride length than a walk). Timbo was right though, technically, you're not doing any work at all, but anyone who's done it knows better.


Guys, there seems to be a lot of confusion on the work/no work issue here...

When walking/running: You have to keep accelerating basically, since otherwise friction and other little nifty things will make you stop. A lot of the equations people are throwing around work great in the "ideal" situation, but any "real world" issue doesnt fall into that category.

When lifting: Mike, - yes in principle you move the bar from A to B and back to A in many lifts, so the net energy change of the bar after one repetition is 0. However you sure did the work (assuming you are loading the bar properly....:)).

First of all you are working against gravity both in the concentric and eccentric part: Accelerating against gravity when moving it up, and also accelerating against gravity in order to stop it from simply falling back down on the eccentric part.

The trick is to remember that we are not dealing with a purely mechanical system, - add in chemical energy transformations and thermic energy and you have the answer.


This is quoted from HowStuffWorks.Com

What is Work?
The work we are talking about here is work in the physics sense. Not home work, or chores, or your job or any other type of work. It is good old mechanical work.

Work is simply the application of a force over a distance, with one catch -- the distance only counts if it is in the direction of the force you apply. Lifting a weight from the ground and putting it on a shelf is a good example of work. The force is equal to the weight of the object, and the distance is equal to the height of the shelf. If the weight were in another room, and you had to pick it up and walk across the room before you put it on the shelf, you didn't do any more work than if the weight were sitting on the ground directly beneath the shelf. It may have felt like you did more work, but while you were walking with the weight you moved horizontally, while the force from the weight was vertical.

Your car also does work. When it is moving, it has to apply a force to counter the forces of friction and aerodynamic drag. If it drives up a hill, it does the same kind of work that you do when lifting a weight. When it drives back down the hill, however, it gets back the work it did. The hill helps the car drive down.

Work is energy that has been used. When you do work, you use energy. But sometimes the energy you use can be recovered. When the car drives up the hill, the work it does to get to the top helps it get back down. Work and energy are closely related. The units of work are the same as the units of energy, which we will discuss later

Work can be done in the horizontal plane, aslong as the force you are considering is also in that plane or has a component in that plane (i.e. i force applied diagonaly to a box moxing horizontally along the ground).

We have to remember that physics is uses many assumption. For most purposes these assumptions are valid.
I.e we normally take Gravity = 9.81m/s/s but really it changes (slightly) depending on location.

The asumption about running and walking is valid. Assuming everything is constant except velocity and time. But in reality this isnt quite true. Its just a basic assumption.

I can walk alot further in a day that i could run. given the same food input.

DD90 - you make a very good point. The human body is not purely a mechanical system.


Good point DD90, most physics is based on perfectly efficient machines and I don't think there are any truly efficient machines like this, which is why most physics is theoretical


In most cases, the energy requirements will be very similar for the shorter distances that most of us travel for our cardio.

Some studies actually misreprent this and say that you burn more calories when you walk slowly. (This is true in total, but when you subtract baseline energy expenditure - the stuff that keeps your body alive, you see that the numbers are actually quite similar between walking and running).

In the end, we all want to be time efficient in the gym and walking just isn't the ideal ticket. I realize that there are a lot of other considerations that you've mentioned - another one would be the stretch shortening cycle which plays a much bigger role in running than walking. It might actually make you more efficient while running.


I've been interested in the same thing except when it is applied to payload, or lifting. I'm guessing at this but I'd say that if you are in tip top shape running or walking you will probably burn just about the same amount of calories either way. But if you are in crap shape then running is going to burn way more calories to a point and then backfire. Another point is that the actual stress of running is going to cause more damage to the body even if you are in good shape. The recovery from that stress is going to require more energy than walking would. I'm shooting in the dark here but that is my assumtion.


Actually all the laws/equations are valid for "real world" applications, - its simply the assumptions that let you discard influences like friction etc. which become invalid. This means that the expressions become a bit more complicated, and not always analytically solvable. However most systems of differentail equations can be solved numerically, which is why classical mechanics is the base of an applied field like biomechanics.


JN, Wouldnt walking be more efficient? other wise we would probaly run everywhere! the pendulum effect of the swinging leg, the elastic enegery in the calf etc would have to make walking more efficient. im sure the stretch shortening cycle make you more efficient in running compared to the situtation of not have that mehanism, but its not a very likely scenario!


I don't know Whetu, I'd think that it would make more sense evolutionarily to be more efficient at running, because at least from an evolutionary standpoint, running would need to be more effieicient, because if you're running, then there might be something you're running from, which would mean your body would need to conserve energy to run longer and harder. That's just a guess though. I'd agree about the use of classical mechanics as a base for most any other kind of mechanics, I was thinking more along the lines of the basic equations we were discussing here, the W=Fd etc. Because discarding friction and thermic energy and all of the other factors you need to discard makes it more theoretical than applicable, although I do see what you mean, DD90, is there any chance you're a physicist (or an engineer), you seem to know your stuff here, and know it better than most.


Whetu - I was just throwing out another idea. Even if we were more efficient (able to get further on the same amount of energy) while running, most would choose to walk still because it feels easier.


Mike, Im a biophysicist - now working in computational neuroscience (modelling of neurons and neural systems).

I can follow your evolutional idea a bit, however some other things should be considered: The capabilities of the system/body, and whether you would expect to be running or walking most of the time. Im not sure it would be efficient to perform all movement at high speed,- you'd basically spend to much time/energy switching from a resting to a high-speed regime, and it probably wouldnt be that easy to design/develop a system that is efficient at rest and under extremes (ie. high speed). I guess its easier to have a system thats generally efficient at rest and walking, with the capability of sprinting when necessary....